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Cryptographic System for Performing Secure Iterative Matrix Inversions and Solving Systems of Linear Equations
Cryptographic System for Performing Secure Iterative Matrix Inversions and Solving Systems of Linear Equations
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机译:用于执行安全迭代矩阵求逆的密码系统和线性方程组的求解系统
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摘要
Disclosed embodiments include a cryptographic system implemented in at least one digital computer with one or more processors or hardware such as FPGAs for performing iterative secure computations, analysis, and signal processing directly on encrypted data in untrusted environments. According to a basic embodiment, the proposed cryptographic system comprises: (a) at least one secure protocol for performing matrix multiplications in the encrypted domain, and (b) at least one secure iterative protocol for performing matrix inversions and solving systems of equations based on an iterative secure protocol substantially equivalent to a Newton secure protocol. According to a particular embodiment, the system comprises a plurality of privacy-preserving protocols for solving systems of linear equations (SLE) directly based on homomorphic computation and secret sharing. More specifically, according to a particular embodiment the system uses a secure iterative protocol whereby systems of linear equations and matrix inversions are solved securely and iteratively without imposing any restrictions on the matrix coefficients based on an iterative protocol substantially equivalent to a Newton secure protocol.
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